While the polenta is cooking, heat olive oil over medium-high heat in a large sauté pan; add garlic and cook until fragrant. Add the greens and cook, turning several times, until wilted and tender, about 10 minutes. Transfer to a colander and, using a spoon, press against the greens to remove all the liquid. Fluff the greens and place the colander over a pan of hot water and cover to keep warm.

Meanwhile, poach the eggs: Fill a large, shallow pan with warm water, cover to keep warm and set aside. In a large sauté pan or deep frying pan, pour in water to a depth of 1½ inches. Add the vinegar and 1 teaspoon salt. Bring to a simmer over medium heat. Working in 2 or 3 batches, break the eggs, one at a time, into a small bowl or cup and carefully  slip each egg into the barely simmering water. Using a kitchen spoon, ease the whites as close to the yolks as possible. When the whites have firmed up a little, spoon the barely simmering water over the eggs and continue to cook until the whites are just set and the yolks are glazed over but still liquid, 3 to 5 minutes.

Using a slotted spoon or spatula, carefully transfer the eggs to the pan of warm water. 

To serve, divide the greens among four warmed plates. Carefully place two eggs atop the greens; sprinkle with a little salt and pepper. Serve the hot polenta onto each plate. Top with some of the remaining cheese and serve at once. Pass the rest of the cheese in a bowl.